24 ARYABHATIYA

no example of the working of the rule according to
his interpretation. To what do the words "square"
and "non-square" of his translation refer? The words
of Aryabhata exactly fit the method employed in later
Indian mathematics. Although Brahmagupta does
not give a rule for square root, his method for cube
root is that described below, although the wording of
his rule is different from that of Aryabhata's. I fail to
see any similarity to the rule and method of Theon
of Alexandria.

In the following example the sign ° indicates the
varga places, and the sign - indicates the avarga
places.

15129 (root = l
Square of the root 1

Twice the root 2) 05 (2=quotient (or next digit of root)

(2X1) 4

11

Square of the quotient 4

Twice the root 24)72(3=quotient (m next digit of root)

^2X12) 72

09

Square of the quotient 9

0

Square root is 1 2 3

5. One should divide the second aghana by three times the
square of the (cube) root of the (preceding) ghana. The square
(of the quotient) multiplied by three times the purva (that part
of the cube root already found) is to be subtracted from the first